Playing Ahsoka for the first time. Can I grab a crate and leap with it? Will it cost me movement in this case?

Sure thing! Taking a carte requires an action (unless you play on nal hutta, in that case it costs 2 movement points), then you can use the second action to leap and place her 6 spaces away

Cheers! This seems like an awfully strong piece in tournaments.

She is definitely strong indeed, although she still has to find her stable place into top lists

Any token a figure carries (see retrieve) moves with the figure.

Any token you have claimed stays in your play area when any of your figures move.

If there's something else to the question, let us know.

Force Leap gives no movement points so you have to use a move / interact first then force leap off with it